Chapter 8.8, Problem 16E

To determine

To solve:

The given linear system of equations by graphing.

Answer to Problem 16E

The solution for given system of equations would be $(-4,0)$ .

Explanation of Solution

Given:

A system of equations:

  $\begin{array}{l}2x+y=-8\\ -x+y=4\end{array}$

Calculation:

First of all, we will convert our given equations in slope-intercept form as:

  $\begin{array}{l}2x+y=-8\left(\text{Given equation}\right)\\ 2x-2x+y=-8-2x\left(\text{Subtracting }2x\text{ from both sides}\right)\\ y=-2x-8\end{array}$

  $\begin{array}{l}-x+y=4\left(\text{Given equation}\right)\\ -x+x+y=4+x\left(\text{Adding }x\text{ on both sides}\right)\\ y=x+4\end{array}$

Upon graphing both equations, we will get our required graph as shown below:

  

Upon looking at our graph, we can see that both lines intersect at point $(-4,0)$ . Therefore, the solution for given system of equations would be $(-4,0)$ .